Remark 2.6 
The description of the unstable strata in [1]} was originally only described for varieties. For a scheme \(Y\) , one uses the linearisation \(\mathcal {L}\)  to \(G\) -equivariantly embed \(Y\)  into \(\mathbb {P}^n\)  and then constructs a scheme theoretic stratification of \(Y\)  by taking the fibre product inside \(\mathbb {P}^n\)  of \(Y\)  with the strata in \(\mathbb {P}^n\) , which are locally closed subvarieties of \(\mathbb {P}^n\)  (see [2]}).

